An Adaptive Attitude Control Formulation under Angular Velocity Constraints
|
|
- Jocelyn Strickland
- 7 years ago
- Views:
Transcription
1 An Adaptive Attitude Control Formulation under Angular Velocity Constraints Puneet Singla and Tarunraj Singh An adaptive attitude control law which explicitly takes into account the constraints on individual angular velocity components has been developed for rigid body attitude control problem. Rigorous stability analysis is presented in the paper which guarantee the asymptotic stability of the controller. The performance of the control laws for stable, bounded tracking of attitude trajectories is evaluated. The essential ideas and results from computer simulations are presented to illustrate the performance of the controller developed in this paper. I. Introduction Attitude control is the process of re-orienting a rigid body to a desired attitude or orientation and plays an important role in many applications ranging from various space and air transportation missions (autonomous mid-air re-fueling of an aircraft, International Space Station (ISS) supply and repair, and space systems automated inspection, servicing and assembly), to the control of robotic manipulators. Some of these applications such as mid-air aircraft refueling and space system automated inspection requires very precise rotational maneuvers. These requirements frequently necessitate the use of non-linear rigid body dynamic models for control system design. The attitude motion of a rigid body can be well represented by Euler s equations, 2 for nonlinear relative angular velocity evolution and attitude parameter kinematic equations. The rigid body attitude can be represented by many coordinate choices, 3, 4 but the quaternion representation is an ideal choice for the attitude estimation as it is free of geometrical singularities which is a desirable property when representing large angle amplitude trajectories. Although attitude kinematic and Euler s dynamic equations represent a near-exact dynamical model, for control design purposes, complications may arise from uncertain rigid body inertia which can change due to fuel consumption, solar array deployment, payload variation etc. Furthermore, stability robustness due to model errors and disturbances are primary consideration for design of any autonomous control system. Rigid body attitude control problems have been studied extensively in the literature. 5 Ref. 2 presents a very detailed review of earlier work for rigid-body attitude control problem. In Refs. 6, 8, 9 optimal attitude control laws are presented and in Refs. 5, 6,, 3 Lyapunov analysis based adaptive attitude tracking control Assistant Professor, AIAA, AAS Member, Department of Mechanical & Aerospace Engineering, University at Buffalo, Buffalo, NY-426, psingla@buffalo.edu. Professor, Department of Mechanical & Aerospace Engineering, University at Buffalo, Buffalo, NY-426, tsingh@buffalo.edu. of 2
2 schemes are presented to compensate for the unknown rigid body inertia matrix. Although much progress has been made in rigid body attitude control in the presence of the rigid body inertia matrix uncertainties and external disturbances, there are no means of incorporating constraints on individual angular velocity. Constraints on rigid body angular velocity might be required for many applications such as rendezvous of space shuttle with ISS and mid-air refueling of an aircraft. The main objective of this paper is to develop an adaptive attitude control law to compensate for any errors in inertia matrix which takes into account the constraints on individual components of rigid body angular velocity. The adaptive control formulation in this paper is based upon Lyapunov s direct stability theorem and imposes the exact kinematic equations at the velocity level while taking care of model uncertainties at the acceleration level. An important contribution of the paper is the explicit consideration of constraints on rigid body angular velocity. The structure of this paper is as follows. First, the dynamical models for rigid body rotational motion is set forth followed by the development of adaptive attitude control law. Finally, the controllers designed in this paper are tested using numerical simulations. II. Attitude Dynamics In this section, we set forth the nonlinear rigid body dynamics model that we adopt for attitude kinematics and rotational dynamics. This model is described in order to be specific in the further developments contained in this paper. Rigid body kinematics can be represented by many coordinate choices, 3 but we prefer to use quaternion representation for attitude control since it is free of all geometrical singularities and has linear kinematic differential equations. The attitude motion of a rigid body is represented by nonlinear Euler s equations for angular velocity evolution and quaternion kinematic equations as given below: Quaternion Kinematics: q = 2 Ω(ω)q = 2 B(q)ω Euler s Equations: I ω = u ωiω (a) (b) where, q R 4 is a vector of quaternion that parameterize the rigid body attitude with respect to an inertial frame and ω R 3 represents the rigid body angular velocity expressed in the rigid body frame. u R 3 represents the vector of external torques. Further, I R 3 3 represents the rigid body inertia matrix, and 2 of 2
3 ω R 3 3 is a skew-symmetric matrix given as: ω = ω 3 ω 2 ω 3 ω ω 2 ω (2) Finally, Ω(ω) = ω 3 ω 2 ω ω 3 ω ω 2 ω 2 ω ω 3 ω ω 2 ω 3, B(q) = q 4 q 3 q 2 q 3 q 4 q q 2 q q 4 q q 2 q 3 (3a) III. Controller Formulation In this section, the velocity bounded adaptive control law will be derived for attitude control, using Lyapunov s direct stability theorem. The novel feature of the control law developed in this paper is that it explicitly accounts for bounds on uncertain rigid body inertia matrix and rigid body angular velocity. First, we will develop nominal attitude control for bounded rigid body angular velocity and later we will generalize the controller for bounds on uncertain rigid body inertia matrix. A. Feedback Control Formulation For Attitude Motion In this section, we seek to design a feedback control law for the system described by Eqs. (a) and (b) to regulate the rigid body attitude parameterized by reference quaternion q f such that ω (t) k, ω 2 (t) k 2, ω 3 (t) k 3, t (4) For this purpose, we define the error quaternion δq which represents the departure from the reference attitude trajectory q f. δq(t) = q(t) q f = q f 4 I q T f 3 q f3 q f3 q f4 q(t) (5) Making use of attitude kinematic Eq. (a), the attitude error kinematics can be written as: δ q = 2 Ωδq = B(δq)ω (6) 2 3 of 2
4 Now, to find an expression for a stabilizing controller, let us consider a candidate Lyapunov function: V = ( δq 4 ) 2 + δq T 3δq k 4 log 3 ki 2 i= (7) 3 (ki 2 ω2 i ) where, k, k 2 and k 3 are positive constant. We mention that the log-term in our Lyapunov function is motivated by the Lyapunov function introduced in Ref. [4]. Now, differentiating V with respect to time and making use of the fact that Ω(ω) is a skew-symmetric matrix leads to following expression for i= V : V = δq T 3ω + k 4 ω T k 2 ω2 k 2 2 ω2 2 k 2 3 ω2 3 ω (8) Now, substituting for ω from Eq. (b) in the above expression leads to V = δq T 3ω + k 4 ω T k 2 ω2 k 2 2 ω2 2 k 2 3 ω2 3 I ( ωiω + u) (9) Now, making use of the fact that ω is a skew-symmetric matrix, we get the following expression for V Now, if we choose control law to be V = δq T 3ω + k 4 ω T k 2 ω2 k 2 2 ω2 2 k 2 3 ω2 3 I u () u = IK ω (δq 3 + k 8 ω), K ω = k 4 k 2 ω2 k 4 k 2 2 ω2 2 k 4 k 2 3 ω2 3 () then V reduces to the following negative semi-definite function V = k 8 ω T ω (2) 4 of 2
5 It is clear that V is positive definite for the domain where ω has to lie within the hyper-rectangle with sides 2k i, i =, 2, 3. Thus, we can state that: ω i k i, i =, 2, 3 (3) Since V and V >, V is only negative semi-definite. However, we can easily show that δq, ω L. 5, 6 Further from the integral of Eq. (2), it follows that ω L L 2 and therefore from Barbalat s Lemma ω as t. Finally, using LaSalle s invariance principle 6 3, 5 we can show that δq as t. IV. Adaptation Law for Uncertain Inertia Matrix In this section, we seek to develop adaptation laws for inertia matrix I along with control law developed in the previous section to take care of any uncertainties in the inertia matrix. Let Î be the estimated value of the inertia matrix and I the inertia error matrix defined as follows: I = Î I (4) Further, we define a new variable J = I and analogous to I, we define: J = Ĵ J (5) Furthermore to enforce the symmetry constraint of J, we define a 6 vector: Θ = { J, J 2, J 3, J 22, J 23, J 33, } (6) Further, we make use of principle of equivalence 6 and assume that the expression for control vector of Eq. () is still valid. As a consequence of this, the applied control can be written as: u = ÎK ω (δq 3 + k 8 ω) (7) where, K ω = k 4 k 2 ω2 k 4 k 2 2 ω2 2 k 4 k 2 3 ω2 3 (8) 5 of 2
6 Now, let us consider a candidate Lyapunov function: V = ( δq 4 ) 2 + δq T 3δq k 4 log 3 ki 2 i= + 3 (ki 2 ω2 i ) i= 2 ΘT Γ Θ (9) Differentiating the above expression w.r.t. t and using the fact that ω is a skew-symmetric matrix leads to the following expression for V V = δq T 3ω + ω T K ω I u + Θ T Γ Θ (2) Now, substituting for u from Eq. (7) leads to [ ] V = δq T 3ω + ω T K ω I ÎK ω (δq 3 + k 8 ω) + Θ T Γ Θ (2a) Now, making use of Eq. (5), we have: ) I Î = JĴ = (Ĵ J Ĵ = JÎ, = (22a) Now, substitution of Eq. (22a) in Eq. (2a) leads to ) V = δq T 3ω ω T K ω ( JÎ K ω (δq 3 + k 8 ω) + Θ T Γ Θ = k 8 ω T ω + ω T K ω JÎK ω (δq 3 + k 8 ω) + Θ T Γ Θ (23a) Further, we can write: y y 2 y 3 JK ω ω = MΘ, M = y y 2 y 3, y = K ω ω (24) y y 2 y 3 Now, substitution of Eq. 24 in Eq. 23a leads to V = k 8 ω T ω + Θ T M T ÎK ω (δq 3 + k 8 ω) + Θ T Γ Θ (25a) 6 of 2
7 So, if we choose adaptation law to be Θ = ΓM T ÎK ω (δq 3 + k 8 ω) (26) Then, V reduces to the following negative semi-definite function: V = k 8 ω T ω (27) Since V and V >, V is only negative semi-definite. Once again, we can easily show that δq, ω, Θ L. 5, 6 Further from the integral of Eq. (27), it follows that ω L L 2 and therefore from Barbalat s Lemma ω as t. Finally, using LaSalle s invariance principle 6 3, 5 we can show that δq as t. Further, notice that it is easy to construct Ĵ = J from the expression for Θ and further, an expression for Î can be obtained by making use of the fact that ÎĴ = : ÎĴ + Î Ĵ = Î = Î ĴÎ (28a) (28b) Finally, notice that we can only guarantee that Θ L which means that estimated inertia matrix is bounded and there is no guarantee that estimated inertia matrix will converge to the true inertia matrix. Furthermore, one can invoke parameter projection 6 to guarantee that Ĵ is non-singular and positive-definite. V. Numerical Results The control laws presented in this paper are illustrated in this section for a particular attitude regulating maneuver. We consider following two simulation test cases with different initial conditions to demonstrate the effectiveness of the adaptive control laws. Test Case : q(t ) = {,,, } T, q(t f ) = {,.5, } T.75, ω(t ) = {,, } T, ω(t f ) = {,, } T Test Case 2: q(t ) = {,,, } T, q(t f ) = {,.5, } T.75, ω(t ) = {3, 3, 3} T, ω(t f ) = {,, } T 7 of 2
8 The angular velocity bounds for both the test cases are chosen to be: k = k 2 = k 3 = 4rad/sec. The true and initial inertia matrices of the rigid body are assumed to be: I = , Î = The various tuning parameters for the adaptive controllers for both the test cases are selected as follows: Γ = 2, k 8 =.5, k 4 = We mention that the feedback gain k 8 is deliberately chosen to be a small number so that inertia matrix term in the controller expression can dominate the pure feedback term. Fig. shows the various plots for the test case. Figs. (a) and (b) show the rigid body attitude (q) and angular velocity (ω), respectively. The corresponding commanded control input is shown in Fig. (c). The blue dashed line in these plot corresponds to control law without adapting for various inertia parameters while the red solid line in these plots corresponds to adaptive control law. From these plots it is clear that attitude error goes to zero over the time and rigid body angular velocity is well with in the prescribed bounds. Further, Fig. (d) shows the plots of estimated rigid body inertia parameters corresponding to update law of Eq. (26). From these plots, it is clear that the regulation performance of the controllers is marginally better with the adaptation of uncertain inertia matrix for test case. To show the effectiveness of the adaptation laws, let us consider the simulation results for test case 2 shown in Fig. 2. Figs. 2(a) and 2(b) show the rigid body attitude (q) and angular velocity (ω) plots for test case 2, respectively. The corresponding commanded control input is shown in Fig. 2(c). Once again, the blue dashed line in these plot corresponds to control law without adapting for various inertia parameters while the red solid line in these plots corresponds to adaptive control law. From these plots it is clear that although rigid body angular velocity is well with in the prescribed bounds with or without the adaptation of inertia matrix but attitude and angular velocity error converge to zero when the adaptation for uncertain inertia matrix is on. Further, Fig. (d) shows the plots of estimated rigid body inertia parameters corresponding to update law of Eq. (26). From these plots, it is clear that the regulation performance of the controllers is much better with the adaptation of uncertain inertia matrix for test case 2. It is worthwhile to notice 8 of 2
9 q.5 Adaptation off Adaptation on q 2 q 3 q 4 (a) q vs. ω 3 ω ω Adaptation off Adaptation on (b) ω vs. 2 u u u (c) u vs Δ I ij (d) I ij vs. Figure. Simulation Results for Test Case. 9 of 2
10 that the only difference between the two test cases is the initial conditions for the angular velocity vector ω. These results completely support the theoretical result that performance of the controller can be improved with the adaptation of unknown inertia matrix. VI. Concluding Remarks An asymptotically stable adaptive controller has been designed for rigid body attitude control which explicitly takes into consideration the bounds on angular velocity. The adaptive control formulations in this paper is based upon Lyapunov s direct stability theorem and imposes the exact kinematic equations at the velocity level while taking care of model uncertainties at the acceleration level. The proposed control law is shown to work well in the presence of bounded angular velocity constraints fully consistent with the asymptotic stability analysis presented. While, the simulation results presented in this paper merely illustrate formulations for a particular attitude maneuver, further testing would be required to reach any conclusions about the efficacy of the control and adaptation laws for tracking arbitrary maneuvers. References Schaub, H. and Junkins, J. L., Analytical Mechanics of Space Systems, AIAA Education Series, AIAA, Junkins, J. L. and Turner, J. D., Optimal Spacecraft Rotational Maneuvers, Elsevier Science Publishers, Shuster, M. D., A Survey of Attitude Representations, Journal of the Astronautical Sciences, Vol. 4, No. 4, October December 993, pp Junkins, J. L. and Singla, P., How Nonlinear Is It? A Tutorial on Nonlinearity of Orbit and Attitude Dynamics, Journal of Astronautical Sciences, Vol. 52, No. -2, 24, pp. 7 6, keynote paper. 5 Schaub, H., Akella, M., and Junkins, J. L., Adaptive Control of Nonlinear Attitude Motions Realizing Linear Closed Loop Dynamics, AIAA Journal of Guidance, Control, and Dynamics, Vol. 24, No., 2, pp Carrington, C. K. and Junkins, J. L., Optimal nonlinear feedback control for spacecraft attitude maneuvers, AIAA Journal of Guidance, Control, and Dynamics, Vol. 9, No., 986, pp Tsiotras, P., Further Passivity Results for the Attitude Control Problem, IEEE Transactions on Automatic Contorl, Vol. 43, No., Nov 998, pp Krstic, M. and Tsiotras, P., Inverse optimality results for the attitude motion of a rigid spacecraft, American Control Conference, 997. Proceedings of the 997, Vol. 3, 4-6 Jun 997, pp vol.3. 9 Tsiotras, P., Stabilization and optimality results for the attitude control problem, AIAA Journal of Guidance, Control, and Dynamics, Vol. 9, No. 4, 996, pp Tsiotras, P., A passivity approach to attitude stabilization using nonredundant kinematic parameterizations, Decision and Control, 995., Proceedings of the 34th IEEE Conference on, Vol., 3-5 Dec 995, pp vol.. Junkins, J. L., Akella, M. R., and Robinett, R. D., Nonlinear Adaptive Control of Spacecraft Maneuvers, AIAA Journal of Guidance, Control, and Dynamics, Vol. 2, No. 6, 997, pp Wen, J. T. Y. and Kreutz-Delgado, K., The attitude control problem, Automatic Control, IEEE Transactions on, Vol. 36, No., Oct 99, pp of 2
11 q q 2 q 3 q 4 Adaptation off Adaptation on (a) q vs. ω ω 2 ω Adaptation off Adaptation on (b) ω vs. u 5 Adaptation off Adaptation on u u (c) u vs Δ I ij (d) I ij vs. Figure 2. Simulation Results for Test Case 2. of 2
12 3 Tanygin, S., Generalization of Adaptive Attitude Tracking, AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Monterey, CA, USA, August Ngo, K., Mahony, R., and Jiang, Z.-P., Integrator backstepping design for motion systems with velocity constraint, Control Conference, 24. 5th Asian, Vol., July 24, pp Vol.. 5 Sastry, S., Nonlinear Systems: Analysis, Stability and Control, Springer-Verlag, NY, USA, Ionnaou, P. A. and Sun, J., Robust Adaptive Control, Prentice Hall Inc., NJ, of 2
Principal Rotation Representations of Proper NxN Orthogonal Matrices
Principal Rotation Representations of Proper NxN Orthogonal Matrices Hanspeter Schaub Panagiotis siotras John L. Junkins Abstract hree and four parameter representations of x orthogonal matrices are extended
More informationSpacecraft Dynamics and Control. An Introduction
Brochure More information from http://www.researchandmarkets.com/reports/2328050/ Spacecraft Dynamics and Control. An Introduction Description: Provides the basics of spacecraft orbital dynamics plus attitude
More informationDesign-Simulation-Optimization Package for a Generic 6-DOF Manipulator with a Spherical Wrist
Design-Simulation-Optimization Package for a Generic 6-DOF Manipulator with a Spherical Wrist MHER GRIGORIAN, TAREK SOBH Department of Computer Science and Engineering, U. of Bridgeport, USA ABSTRACT Robot
More informationCONTRIBUTIONS TO THE AUTOMATIC CONTROL OF AERIAL VEHICLES
1 / 23 CONTRIBUTIONS TO THE AUTOMATIC CONTROL OF AERIAL VEHICLES MINH DUC HUA 1 1 INRIA Sophia Antipolis, AROBAS team I3S-CNRS Sophia Antipolis, CONDOR team Project ANR SCUAV Supervisors: Pascal MORIN,
More informationDynamics. Basilio Bona. DAUIN-Politecnico di Torino. Basilio Bona (DAUIN-Politecnico di Torino) Dynamics 2009 1 / 30
Dynamics Basilio Bona DAUIN-Politecnico di Torino 2009 Basilio Bona (DAUIN-Politecnico di Torino) Dynamics 2009 1 / 30 Dynamics - Introduction In order to determine the dynamics of a manipulator, it is
More informationOperational Space Control for A Scara Robot
Operational Space Control for A Scara Robot Francisco Franco Obando D., Pablo Eduardo Caicedo R., Oscar Andrés Vivas A. Universidad del Cauca, {fobando, pacaicedo, avivas }@unicauca.edu.co Abstract This
More informationMECH 5105 Orbital Mechanics and Control. Steve Ulrich Carleton University Ottawa, ON, Canada
MECH 5105 Orbital Mechanics and Control Steve Ulrich Carleton University Ottawa, ON, Canada 2 Copyright c 2015 by Steve Ulrich 3 4 Course Outline About the Author Steve Ulrich is an Assistant Professor
More informationINSTRUCTOR WORKBOOK Quanser Robotics Package for Education for MATLAB /Simulink Users
INSTRUCTOR WORKBOOK for MATLAB /Simulink Users Developed by: Amir Haddadi, Ph.D., Quanser Peter Martin, M.A.SC., Quanser Quanser educational solutions are powered by: CAPTIVATE. MOTIVATE. GRADUATE. PREFACE
More information2. Dynamics, Control and Trajectory Following
2. Dynamics, Control and Trajectory Following This module Flying vehicles: how do they work? Quick refresher on aircraft dynamics with reference to the magical flying space potato How I learned to stop
More informationAMIT K. SANYAL. 2001-2004 Ph.D. in Aerospace Engineering, University of Michigan, Ann Arbor, MI. Date of completion:
AMIT K. SANYAL Office Home 305 Holmes Hall 3029 Lowrey Avenue Mechanical Engineering Apartment # N-2211 University of Hawaii at Manoa Honolulu, HI 96822 Honolulu, HI 96822 480-603-8938 808-956-2142 aksanyal@hawaii.edu
More informationStability Analysis of Small Satellite Formation Flying and Reconfiguration Missions in Deep Space
Stability Analysis of Small Satellite Formation Flying and Reconfiguration Missions in Deep Space Saptarshi Bandyopadhyay, Chakravarthini M. Saaj, and Bijnan Bandyopadhyay, Member, IEEE Abstract Close-proximity
More informationLinear-Quadratic Optimal Controller 10.3 Optimal Linear Control Systems
Linear-Quadratic Optimal Controller 10.3 Optimal Linear Control Systems In Chapters 8 and 9 of this book we have designed dynamic controllers such that the closed-loop systems display the desired transient
More informationResearch Article End-Effector Trajectory Tracking Control of Space Robot with L 2 Gain Performance
Mathematical Problems in Engineering Volume 5, Article ID 7534, 9 pages http://dx.doi.org/.55/5/7534 Research Article End-Effector Trajectory Tracking Control of Space Robot with L Gain Performance Haibo
More informationForce/position control of a robotic system for transcranial magnetic stimulation
Force/position control of a robotic system for transcranial magnetic stimulation W.N. Wan Zakaria School of Mechanical and System Engineering Newcastle University Abstract To develop a force control scheme
More information4 Lyapunov Stability Theory
4 Lyapunov Stability Theory In this section we review the tools of Lyapunov stability theory. These tools will be used in the next section to analyze the stability properties of a robot controller. We
More informationOptimal Design of α-β-(γ) Filters
Optimal Design of --(γ) Filters Dirk Tenne Tarunraj Singh, Center for Multisource Information Fusion State University of New York at Buffalo Buffalo, NY 426 Abstract Optimal sets of the smoothing parameter
More informationDimension Theory for Ordinary Differential Equations
Vladimir A. Boichenko, Gennadij A. Leonov, Volker Reitmann Dimension Theory for Ordinary Differential Equations Teubner Contents Singular values, exterior calculus and Lozinskii-norms 15 1 Singular values
More informationRotation: Moment of Inertia and Torque
Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn
More informationOptimal Reconfiguration of Formation Flying Satellites
Proceedings of the th IEEE Conference on Decision and Control, and the European Control Conference 5 Seville, Spain, December -5, 5 MoA.6 Optimal Reconfiguration of Formation Flying Satellites Oliver Junge
More informationExample 4.1 (nonlinear pendulum dynamics with friction) Figure 4.1: Pendulum. asin. k, a, and b. We study stability of the origin x
Lecture 4. LaSalle s Invariance Principle We begin with a motivating eample. Eample 4.1 (nonlinear pendulum dynamics with friction) Figure 4.1: Pendulum Dynamics of a pendulum with friction can be written
More informationA PAIR OF MEASURES OF ROTATIONAL ERROR FOR AXISYMMETRIC ROBOT END-EFFECTORS
A PAIR OF MEASURES OF ROTATIONAL ERROR FOR AXISYMMETRIC ROBOT END-EFFECTORS Sébastien Briot, Ilian A. Bonev Department of Automated Manufacturing Engineering École de technologie supérieure (ÉTS), Montreal,
More informationA Control Scheme for Industrial Robots Using Artificial Neural Networks
A Control Scheme for Industrial Robots Using Artificial Neural Networks M. Dinary, Abou-Hashema M. El-Sayed, Abdel Badie Sharkawy, and G. Abouelmagd unknown dynamical plant is investigated. A layered neural
More informationMotion Control of 3 Degree-of-Freedom Direct-Drive Robot. Rutchanee Gullayanon
Motion Control of 3 Degree-of-Freedom Direct-Drive Robot A Thesis Presented to The Academic Faculty by Rutchanee Gullayanon In Partial Fulfillment of the Requirements for the Degree Master of Engineering
More informationVéronique PERDEREAU ISIR UPMC 6 mars 2013
Véronique PERDEREAU ISIR UPMC mars 2013 Conventional methods applied to rehabilitation robotics Véronique Perdereau 2 Reference Robot force control by Bruno Siciliano & Luigi Villani Kluwer Academic Publishers
More informationSimulation of Trajectories and Comparison of Joint Variables for Robotic Manipulator Using Multibody Dynamics (MBD)
Simulation of Trajectories and Comparison of Joint Variables for Robotic Manipulator Using Multibody Dynamics (MBD) Jatin Dave Assistant Professor Nirma University Mechanical Engineering Department, Institute
More informationStabilizing a Gimbal Platform using Self-Tuning Fuzzy PID Controller
Stabilizing a Gimbal Platform using Self-Tuning Fuzzy PID Controller Nourallah Ghaeminezhad Collage Of Automation Engineering Nuaa Nanjing China Wang Daobo Collage Of Automation Engineering Nuaa Nanjing
More informationMetrics on SO(3) and Inverse Kinematics
Mathematical Foundations of Computer Graphics and Vision Metrics on SO(3) and Inverse Kinematics Luca Ballan Institute of Visual Computing Optimization on Manifolds Descent approach d is a ascent direction
More informationOrigins of the Unusual Space Shuttle Quaternion Definition
47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition 5-8 January 2009, Orlando, Florida AIAA 2009-43 Origins of the Unusual Space Shuttle Quaternion Definition
More informationPrecise Modelling of a Gantry Crane System Including Friction, 3D Angular Swing and Hoisting Cable Flexibility
Precise Modelling of a Gantry Crane System Including Friction, 3D Angular Swing and Hoisting Cable Flexibility Renuka V. S. & Abraham T Mathew Electrical Engineering Department, NIT Calicut E-mail : renuka_mee@nitc.ac.in,
More informationLeast-Squares Intersection of Lines
Least-Squares Intersection of Lines Johannes Traa - UIUC 2013 This write-up derives the least-squares solution for the intersection of lines. In the general case, a set of lines will not intersect at a
More informationOnline Tuning of Artificial Neural Networks for Induction Motor Control
Online Tuning of Artificial Neural Networks for Induction Motor Control A THESIS Submitted by RAMA KRISHNA MAYIRI (M060156EE) In partial fulfillment of the requirements for the award of the Degree of MASTER
More informationLecture L22-2D Rigid Body Dynamics: Work and Energy
J. Peraire, S. Widnall 6.07 Dynamics Fall 008 Version.0 Lecture L - D Rigid Body Dynamics: Work and Energy In this lecture, we will revisit the principle of work and energy introduced in lecture L-3 for
More informationA Passivity Measure Of Systems In Cascade Based On Passivity Indices
49th IEEE Conference on Decision and Control December 5-7, Hilton Atlanta Hotel, Atlanta, GA, USA A Passivity Measure Of Systems In Cascade Based On Passivity Indices Han Yu and Panos J Antsaklis Abstract
More informationOn Motion of Robot End-Effector using the Curvature Theory of Timelike Ruled Surfaces with Timelike Directrix
Malaysian Journal of Mathematical Sciences 8(2): 89-204 (204) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Journal homepage: http://einspem.upm.edu.my/journal On Motion of Robot End-Effector using the Curvature
More informationGeometric Adaptive Control of Quadrotor UAVs Transporting a Cable-Suspended Rigid Body
Geometric Adaptive Control of Quadrotor UAVs Transporting a Cable-Suspended Rigid Body Taeyoung Lee Abstract This paper is focused on tracking control for a rigid body payload that is connected to an arbitrary
More informationSystem Modeling and Control for Mechanical Engineers
Session 1655 System Modeling and Control for Mechanical Engineers Hugh Jack, Associate Professor Padnos School of Engineering Grand Valley State University Grand Rapids, MI email: jackh@gvsu.edu Abstract
More informationIntroduction to Engineering System Dynamics
CHAPTER 0 Introduction to Engineering System Dynamics 0.1 INTRODUCTION The objective of an engineering analysis of a dynamic system is prediction of its behaviour or performance. Real dynamic systems are
More informationACTUATOR DESIGN FOR ARC WELDING ROBOT
ACTUATOR DESIGN FOR ARC WELDING ROBOT 1 Anurag Verma, 2 M. M. Gor* 1 G.H Patel College of Engineering & Technology, V.V.Nagar-388120, Gujarat, India 2 Parul Institute of Engineering & Technology, Limda-391760,
More informationA New Nature-inspired Algorithm for Load Balancing
A New Nature-inspired Algorithm for Load Balancing Xiang Feng East China University of Science and Technology Shanghai, China 200237 Email: xfeng{@ecusteducn, @cshkuhk} Francis CM Lau The University of
More informationTHE UNIVERSITY OF TEXAS AT AUSTIN Department of Aerospace Engineering and Engineering Mechanics. EM 311M - DYNAMICS Spring 2012 SYLLABUS
THE UNIVERSITY OF TEXAS AT AUSTIN Department of Aerospace Engineering and Engineering Mechanics EM 311M - DYNAMICS Spring 2012 SYLLABUS UNIQUE NUMBERS: 13815, 13820, 13825, 13830 INSTRUCTOR: TIME: Dr.
More informationCIS 536/636 Introduction to Computer Graphics. Kansas State University. CIS 536/636 Introduction to Computer Graphics
2 Lecture Outline Animation 2 of 3: Rotations, Quaternions Dynamics & Kinematics William H. Hsu Department of Computing and Information Sciences, KSU KSOL course pages: http://bit.ly/hgvxlh / http://bit.ly/evizre
More informationBasic Principles of Inertial Navigation. Seminar on inertial navigation systems Tampere University of Technology
Basic Principles of Inertial Navigation Seminar on inertial navigation systems Tampere University of Technology 1 The five basic forms of navigation Pilotage, which essentially relies on recognizing landmarks
More informationGeneral model of a structure-borne sound source and its application to shock vibration
General model of a structure-borne sound source and its application to shock vibration Y. Bobrovnitskii and T. Tomilina Mechanical Engineering Research Institute, 4, M. Kharitonievky Str., 101990 Moscow,
More informationComputer Animation. Lecture 2. Basics of Character Animation
Computer Animation Lecture 2. Basics of Character Animation Taku Komura Overview Character Animation Posture representation Hierarchical structure of the body Joint types Translational, hinge, universal,
More informationWorldwide, space agencies are increasingly exploiting multi-body dynamical structures for their most
Coupled Orbit-Attitude Dynamics in the Three-Body Problem: a Family of Orbit-Attitude Periodic Solutions Davide Guzzetti and Kathleen C. Howell Purdue University, Armstrong Hall of Engineering, 71 W. Stadium
More informationAdvantages of Auto-tuning for Servo-motors
Advantages of for Servo-motors Executive summary The same way that 2 years ago computer science introduced plug and play, where devices would selfadjust to existing system hardware, industrial motion control
More informationState of Stress at Point
State of Stress at Point Einstein Notation The basic idea of Einstein notation is that a covector and a vector can form a scalar: This is typically written as an explicit sum: According to this convention,
More informationIntelligent Mechatronic Model Reference Theory for Robot Endeffector
, pp.165-172 http://dx.doi.org/10.14257/ijunesst.2015.8.1.15 Intelligent Mechatronic Model Reference Theory for Robot Endeffector Control Mohammad sadegh Dahideh, Mohammad Najafi, AliReza Zarei, Yaser
More informationA Direct Numerical Method for Observability Analysis
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL 15, NO 2, MAY 2000 625 A Direct Numerical Method for Observability Analysis Bei Gou and Ali Abur, Senior Member, IEEE Abstract This paper presents an algebraic method
More informationA MONTE CARLO DISPERSION ANALYSIS OF A ROCKET FLIGHT SIMULATION SOFTWARE
A MONTE CARLO DISPERSION ANALYSIS OF A ROCKET FLIGHT SIMULATION SOFTWARE F. SAGHAFI, M. KHALILIDELSHAD Department of Aerospace Engineering Sharif University of Technology E-mail: saghafi@sharif.edu Tel/Fax:
More information3D Tranformations. CS 4620 Lecture 6. Cornell CS4620 Fall 2013 Lecture 6. 2013 Steve Marschner (with previous instructors James/Bala)
3D Tranformations CS 4620 Lecture 6 1 Translation 2 Translation 2 Translation 2 Translation 2 Scaling 3 Scaling 3 Scaling 3 Scaling 3 Rotation about z axis 4 Rotation about z axis 4 Rotation about x axis
More informationAttitude Control and Dynamics of Solar Sails
Attitude Control and Dynamics of Solar Sails Benjamin L. Diedrich A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics & Astronautics University
More informationRobot Task-Level Programming Language and Simulation
Robot Task-Level Programming Language and Simulation M. Samaka Abstract This paper presents the development of a software application for Off-line robot task programming and simulation. Such application
More informationNumerical Solution of Differential Equations
Numerical Solution of Differential Equations Dr. Alvaro Islas Applications of Calculus I Spring 2008 We live in a world in constant change We live in a world in constant change We live in a world in constant
More informationKinematical Animation. lionel.reveret@inria.fr 2013-14
Kinematical Animation 2013-14 3D animation in CG Goal : capture visual attention Motion of characters Believable Expressive Realism? Controllability Limits of purely physical simulation : - little interactivity
More informationHuman-like Arm Motion Generation for Humanoid Robots Using Motion Capture Database
Human-like Arm Motion Generation for Humanoid Robots Using Motion Capture Database Seungsu Kim, ChangHwan Kim and Jong Hyeon Park School of Mechanical Engineering Hanyang University, Seoul, 133-791, Korea.
More informationCONTROLLABILITY. Chapter 2. 2.1 Reachable Set and Controllability. Suppose we have a linear system described by the state equation
Chapter 2 CONTROLLABILITY 2 Reachable Set and Controllability Suppose we have a linear system described by the state equation ẋ Ax + Bu (2) x() x Consider the following problem For a given vector x in
More informationOrbits of the Lennard-Jones Potential
Orbits of the Lennard-Jones Potential Prashanth S. Venkataram July 28, 2012 1 Introduction The Lennard-Jones potential describes weak interactions between neutral atoms and molecules. Unlike the potentials
More informationOn-line trajectory planning of robot manipulator s end effector in Cartesian Space using quaternions
On-line trajectory planning of robot manipulator s end effector in Cartesian Space using quaternions Ignacio Herrera Aguilar and Daniel Sidobre (iherrera, daniel)@laas.fr LAAS-CNRS Université Paul Sabatier
More informationdspace DSP DS-1104 based State Observer Design for Position Control of DC Servo Motor
dspace DSP DS-1104 based State Observer Design for Position Control of DC Servo Motor Jaswandi Sawant, Divyesh Ginoya Department of Instrumentation and control, College of Engineering, Pune. ABSTRACT This
More informationAdaptive Control for Robot Manipulators Under Ellipsoidal Task Space Constraints
22 IEEE/RSJ International Conference on Intelligent Robots and Systems October 7-2, 22. Vilamoura, Algarve, Portugal Adaptive Control for Robot Manipulators Under Ellipsoidal Task Space Constraints Keng
More informationKinematics and Dynamics of Mechatronic Systems. Wojciech Lisowski. 1 An Introduction
Katedra Robotyki i Mechatroniki Akademia Górniczo-Hutnicza w Krakowie Kinematics and Dynamics of Mechatronic Systems Wojciech Lisowski 1 An Introduction KADOMS KRIM, WIMIR, AGH Kraków 1 The course contents:
More informationEffect of Remote Back-Up Protection System Failure on the Optimum Routine Test Time Interval of Power System Protection
Effect of Remote Back-Up Protection System Failure on the Optimum Routine Test Time Interval of Power System Protection Y. Damchi* and J. Sadeh* (C.A.) Abstract: Appropriate operation of protection system
More informationEffect of Remote Back-Up Protection System Failure on the Optimum Routine Test Time Interval of Power System Protection
Effect of Remote Back-Up Protection System Failure on the Optimum Routine Test Time Interval of Power System Protection Y. Damchi* and J. Sadeh* (C.A.) Abstract: Appropriate operation of protection system
More informationPID, LQR and LQR-PID on a Quadcopter Platform
PID, LQR and LQR-PID on a Quadcopter Platform Lucas M. Argentim unielargentim@fei.edu.br Willian C. Rezende uniewrezende@fei.edu.br Paulo E. Santos psantos@fei.edu.br Renato A. Aguiar preaguiar@fei.edu.br
More informationTime Domain and Frequency Domain Techniques For Multi Shaker Time Waveform Replication
Time Domain and Frequency Domain Techniques For Multi Shaker Time Waveform Replication Thomas Reilly Data Physics Corporation 1741 Technology Drive, Suite 260 San Jose, CA 95110 (408) 216-8440 This paper
More informationanimation animation shape specification as a function of time
animation animation shape specification as a function of time animation representation many ways to represent changes with time intent artistic motion physically-plausible motion efficiency control typically
More informationPre-requisites 2012-2013
Pre-requisites 2012-2013 Engineering Computation The student should be familiar with basic tools in Mathematics and Physics as learned at the High School level and in the first year of Engineering Schools.
More informationDynamics and Control of an Elastic Dumbbell Spacecraft in a Central Gravitational Field
Dynamics Control of an Elastic Dumbbell Spacecraft in a Central Gravitational Field Amit K. Sanyal, Jinglai Shen, N. Harris McClamroch 1 Department of Aerospace Engineering University of Michigan Ann Arbor,
More informationGeometric Constraints
Simulation in Computer Graphics Geometric Constraints Matthias Teschner Computer Science Department University of Freiburg Outline introduction penalty method Lagrange multipliers local constraints University
More informationAdaptive Control Using Combined Online and Background Learning Neural Network
Adaptive Control Using Combined Online and Background Learning Neural Network Eric N. Johnson and Seung-Min Oh Abstract A new adaptive neural network (NN control concept is proposed with proof of stability
More informationInvestigation of Periodic-Disturbance Identification and Rejection in Spacecraft
JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS Vol. 29, No. 4, July August 2006 Investigation of Periodic-Disturbance Identification and Rejection in Spacecraft Jimmy Lau and Sanjay S. Joshi University of
More informationSAMPLE CHAPTERS UNESCO EOLSS PID CONTROL. Araki M. Kyoto University, Japan
PID CONTROL Araki M. Kyoto University, Japan Keywords: feedback control, proportional, integral, derivative, reaction curve, process with self-regulation, integrating process, process model, steady-state
More informationThe Matrix Elements of a 3 3 Orthogonal Matrix Revisited
Physics 116A Winter 2011 The Matrix Elements of a 3 3 Orthogonal Matrix Revisited 1. Introduction In a class handout entitled, Three-Dimensional Proper and Improper Rotation Matrices, I provided a derivation
More informationA Robust Estimator for Almost Global Attitude Feedback Tracking
A Robust Estimator for Almost Global Attitude Feedback Tracking Amit K. Sanyal Nikolaj Nordkvist This article presents a robust and almost global feedback attitude tracking control scheme in conjunction
More informationDrivetech, Inc. Innovations in Motor Control, Drives, and Power Electronics
Drivetech, Inc. Innovations in Motor Control, Drives, and Power Electronics Dal Y. Ohm, Ph.D. - President 25492 Carrington Drive, South Riding, Virginia 20152 Ph: (703) 327-2797 Fax: (703) 327-2747 ohm@drivetechinc.com
More informationFrequency Response of Filters
School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 2 Frequency Response of Filters 1 Introduction Objectives To
More informationLet s first see how precession works in quantitative detail. The system is illustrated below: ...
lecture 20 Topics: Precession of tops Nutation Vectors in the body frame The free symmetric top in the body frame Euler s equations The free symmetric top ala Euler s The tennis racket theorem As you know,
More informationHigh Accuracy Articulated Robots with CNC Control Systems
Copyright 2012 SAE International 2013-01-2292 High Accuracy Articulated Robots with CNC Control Systems Bradley Saund, Russell DeVlieg Electroimpact Inc. ABSTRACT A robotic arm manipulator is often an
More informationIntelligent Submersible Manipulator-Robot, Design, Modeling, Simulation and Motion Optimization for Maritime Robotic Research
20th International Congress on Modelling and Simulation, Adelaide, Australia, 1 6 December 2013 www.mssanz.org.au/modsim2013 Intelligent Submersible Manipulator-Robot, Design, Modeling, Simulation and
More informationSolution of Linear Systems
Chapter 3 Solution of Linear Systems In this chapter we study algorithms for possibly the most commonly occurring problem in scientific computing, the solution of linear systems of equations. We start
More informationIntroduction to Robotics Analysis, Systems, Applications
Introduction to Robotics Analysis, Systems, Applications Saeed B. Niku Mechanical Engineering Department California Polytechnic State University San Luis Obispo Technische Urw/carsMt Darmstadt FACHBEREfCH
More informationω h (t) = Ae t/τ. (3) + 1 = 0 τ =.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.004 Dynamics and Control II Fall 2007 Lecture 2 Solving the Equation of Motion Goals for today Modeling of the 2.004 La s rotational
More informationLyapunov Stability Analysis of Energy Constraint for Intelligent Home Energy Management System
JAIST Reposi https://dspace.j Title Lyapunov stability analysis for intelligent home energy of energ manageme Author(s)Umer, Saher; Tan, Yasuo; Lim, Azman Citation IEICE Technical Report on Ubiquitous
More informationECE 516: System Control Engineering
ECE 516: System Control Engineering This course focuses on the analysis and design of systems control. This course will introduce time-domain systems dynamic control fundamentals and their design issues
More informationAstrodynamics (AERO0024)
Astrodynamics (AERO0024) 6. Interplanetary Trajectories Gaëtan Kerschen Space Structures & Systems Lab (S3L) Course Outline THEMATIC UNIT 1: ORBITAL DYNAMICS Lecture 02: The Two-Body Problem Lecture 03:
More informationLecture L29-3D Rigid Body Dynamics
J. Peraire, S. Widnall 16.07 Dynamics Fall 2009 Version 2.0 Lecture L29-3D Rigid Body Dynamics 3D Rigid Body Dynamics: Euler Angles The difficulty of describing the positions of the body-fixed axis of
More informationPath Tracking for a Miniature Robot
Path Tracking for a Miniature Robot By Martin Lundgren Excerpt from Master s thesis 003 Supervisor: Thomas Hellström Department of Computing Science Umeå University Sweden 1 Path Tracking Path tracking
More information13 MATH FACTS 101. 2 a = 1. 7. The elements of a vector have a graphical interpretation, which is particularly easy to see in two or three dimensions.
3 MATH FACTS 0 3 MATH FACTS 3. Vectors 3.. Definition We use the overhead arrow to denote a column vector, i.e., a linear segment with a direction. For example, in three-space, we write a vector in terms
More informationIsaac Newton s (1642-1727) Laws of Motion
Big Picture 1 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Thomas Peacock 2/7/2007 Lecture 1 Newton s Laws, Cartesian and Polar Coordinates, Dynamics of a Single Particle Big Picture First
More informationConstraint satisfaction and global optimization in robotics
Constraint satisfaction and global optimization in robotics Arnold Neumaier Universität Wien and Jean-Pierre Merlet INRIA Sophia Antipolis 1 The design, validation, and use of robots poses a number of
More informationMulti-Robot Tracking of a Moving Object Using Directional Sensors
Multi-Robot Tracking of a Moving Object Using Directional Sensors Manuel Mazo Jr., Alberto Speranzon, Karl H. Johansson Dept. of Signals, Sensors & Systems Royal Institute of Technology SE- 44 Stockholm,
More informationDEOS. Deutsche Orbitale Servicing Mission. The In-flight Technology Demonstration of Germany s Robotics Approach to Service Satellites
DEOS Deutsche Orbitale Servicing Mission The In-flight Technology Demonstration of Germany s Robotics Approach to Service Satellites B. Sommer, K. Landzettel, T. Wolf, D. Reintsema, German Aerospace Center
More informationCHAPTER 2 ORBITAL DYNAMICS
14 CHAPTER 2 ORBITAL DYNAMICS 2.1 INTRODUCTION This chapter presents definitions of coordinate systems that are used in the satellite, brief description about satellite equations of motion and relative
More informationElgersburg Workshop 2010, 1.-4. März 2010 1. Path-Following for Nonlinear Systems Subject to Constraints Timm Faulwasser
#96230155 2010 Photos.com, ein Unternehmensbereich von Getty Images. Alle Rechte vorbehalten. Steering a Car as a Control Problem Path-Following for Nonlinear Systems Subject to Constraints Chair for Systems
More informationKinematics of Robots. Alba Perez Gracia
Kinematics of Robots Alba Perez Gracia c Draft date August 31, 2007 Contents Contents i 1 Motion: An Introduction 3 1.1 Overview.......................................... 3 1.2 Introduction.........................................
More informationLecture 7: Finding Lyapunov Functions 1
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.243j (Fall 2003): DYNAMICS OF NONLINEAR SYSTEMS by A. Megretski Lecture 7: Finding Lyapunov Functions 1
More informationCONTROL SYSTEMS, ROBOTICS AND AUTOMATION Vol. XVI - Fault Accomodation Using Model Predictive Methods - Jovan D. Bošković and Raman K.
FAULT ACCOMMODATION USING MODEL PREDICTIVE METHODS Scientific Systems Company, Inc., Woburn, Massachusetts, USA. Keywords: Fault accommodation, Model Predictive Control (MPC), Failure Detection, Identification
More informationHow To Understand The Dynamics Of A Multibody System
4 Dynamic Analysis. Mass Matrices and External Forces The formulation of the inertia and external forces appearing at any of the elements of a multibody system, in terms of the dependent coordinates that
More informationActive Vibration Isolation of an Unbalanced Machine Spindle
UCRL-CONF-206108 Active Vibration Isolation of an Unbalanced Machine Spindle D. J. Hopkins, P. Geraghty August 18, 2004 American Society of Precision Engineering Annual Conference Orlando, FL, United States
More information